Having just changed my Apple ID to separate myself from my son who was sharing my ID I can tell you how to handle this in IOS7. I went to the Apple web site and established my new ID.
I followed the advice on this support page to change my Apple ID Change your Apple ID - Apple Support
I then followed the advice on this page to update the ID on my device Sign in with a different Apple ID on your iPhone, iPad, or iPod touch - Apple Support
IMPORTANT!!!! When you delete your iCloud for your old Apple ID off your phone you will lose all your documents that are in the cloud but not your contacts that are out in the cloud. Also, before following the directions on the"Sign in with a Different Account" page to delete the iCloud Apple ID first turn off iCloud sync on each item individually. When you turn off the sync it will ask you if you want to keep the data on your phone. Yes you do want this. After turning off sync individually Delete the iCloud account for the old Apple ID. Then when you then sign into iCloud with your new Apple ID select the Merge option and it will upload all your contacts and data to the iCloud account for your new Apple ID.
If you simply Delete your iCloud account it will delete all your contacts off your phone. If you delete iCloud without first turning sync off Contacts and your contacts are then deleted off your phone, don't worry. Simply log back into iCloud with your old account and your contacts will be restored. Then you can turn off the sync on all items, Delete the old account from iCloud, sign in with the new apple Id, select Merge iPhone data. So it puts your contacts and data from your phone into your new iCloud account.